A Fresh Angle on Groundhop Planning

As regular readers will know (hello, both of you!) I am working my way randomishly through 30 remaining unvisited Step 4 grounds on my list.  Most of them are a fair distance away from Yapp Acres.

Tomorrow’s journey will be geographically decided by events at Ashton Gate tonight.  Bristol City host Bolton Wanderers in the 4^th Round of the FA Cup.

I will go to the ground that is nearest the place of birth of the scorer of the last goal in this game.

The thirteen far-flung possibilities are:

Blackfield & Langley

Brighouse Town

Carlton Town

Cinderford Town

Clitheroe

Melksham Town

Pontefract Collieries

Ramsbottom United

Sevenoaks Town

Slimbridge

Street

Tadcaster Albion

Whyteleafe

If the scorer is UK-born, then Google Maps is my friend and I will take the shortest practicable distance by foot.

If the scorer was born overseas, then the formula below will be used to calculate the central angle of the arc of a “great circle” connecting the two places concerned, P & Q on the diagram.  This will assume that the Earth is a perfect sphere, which isn’t true, but it is close enough for this purpose.  A great circle is always the shortest distance between two points on the surface of a sphere.  The equator is an example – the shortest distance between two points on the equator is always along the equator.  The route is not always a straight line on a conventional map, because of the distortions caused by projecting a curved surface onto paper.  Fascinating stuff, I am sure you’ll agree, and no, I don't need to get out more, thank you.

The length of the arc is directly proportional to the angle, so the smallest angle will be what I am looking for.  The actual distance would be the angle (in radians) multiplied by the radius of the earth.

The formula is:

where Δσ is the central angle we need and Φ and λ are the conventional latitude and longitude for places 1 & 2 measured from the reference points of the equator and Greenwich meridian respectively.  Bear with me, you’ll need all this stuff when you are plotting your private-helicopter groundhopping routes on the back of your promised post-Brexit prosperity.  This blog keeps you ahead of the game either way, because if post-Brexit prosperity turns out to be a dud you can place your bets based on #keepertopcolourstats and hope for the best.  If this happens I will cover home brewing and distillation techniques in a future post.

Small Print: if it is 0-0 then I will go by the place of residence of the match referee as published by the FA.  Own goals also count, based on the place of birth of the own-goalscorer!  Why haven’t I chosen Arsenal v Manchester United?  Well, that lot get enough attention anyway, the bunch of overpaid prima donnas.

Diagram credit:

https://commons.wikimedia.org/wiki/File:Central_angle.svg

Author CheCheDaWaff, Own Work, 30 April 2016 and this file is licensed under the Creative Commons Attribution-Share Alike 4.0 International licence.

Formula credit:

Taken from: https://en.wikipedia.org/wiki/Great-circle_distance

UPDATE:

Mark Beevers (b Barnsley) gave Bolton a short-lived lead before Callum O'Dowda equalised.  Callum is from Kidlington near Oxford and this would have sent me (narrowly) to Slimbridge, just two miles closer than Melksham Town.  However, Niclas Eliasson stepped up with a spectacular winning goal as early as the 30th minute.

As the game neared its conclusion with Bolton still trailing, I checked the birthplace of their goalkeeper Remi Matthews in case there was a classic FA Cup ending to come.  He was born in Gorleston-on-Sea on the east coast and could have sent me to Carlton or Sevenoaks. 

Niclas Eliasson hails from one of the Varbergs in Sweden and fellow groundhopper Laurence Reade helped to confirm that I needed to measure from the settlement on the west coast rather than the eastern village or the Stockholm suburb.  Tadcaster looked the most likely, but with the curvature of the earth to take into account, I have also looked at Carlton (near Nottingham) and Sevenoaks as a check.

Here are the parameters from Excel.  The longitudes and latitudes have been taken from Wikipedia and converted to decimal format.  The angles in degrees are converted to radians before taking the sines and cosines and working out the key angle, delta sigma.  Care is needed over calculating the longitudinal difference because some of the grounds are east of the Greenwich meridian whereas others are to the west.  The SMALLEST delta sigma means the shortest great circle distance across the earth's surface, and Tadcaster Albion wins by about 0.006 of a radian.  Thanks for all the interest!

Place	Lat
Varberg	57.116667
Tadcaster	53.855200
Place	Long
Varberg	12.216667	E
Tadcaster	1.262000	W
sin phi1	0.839778
sin phi2	0.807529
cos phi1	0.542930
cos phi2	0.589828
delta lambda	13.478667
cos delta lambda	0.972457
delta sigma	0.144625
Place	Lat
Varberg	57.116667
Sevenoaks	51.278100
Place	Long
Varberg	12.216667	E
Sevenoaks	0.187400	E
sin phi1	0.839778
sin phi2	0.780191
cos phi1	0.542930
cos phi2	0.625541
delta lambda	12.029267
cos delta lambda	0.978041
delta sigma	0.159198
Place	Lat
Varberg	57.116667
Carlton Town	52.966944
Place	Long
Varberg	12.216667	E
Carlton Town	1.087778	W
sin phi1	0.839778
sin phi2	0.798288
cos phi1	0.542930
cos phi2	0.602276
delta lambda	13.304444
cos delta lambda	0.973161
delta sigma	0.151126